Time delays associated with timed signals received from location determination (LD) signal sources, such as satellites in a Global Positioning System (GPS), Global Orbiting Navigation Satellite System (GLONASS), or other Satellite Positioning System (SATPS), or such as ground-based signal towers in a Loran system, are used to estimate the distance of each LDS signal source from the LDS receiver of such signals. In a conventional approach, a time delay associated with the LDS signal received from each satellite is determined and expressed in code phase as a pseudorange value. The pseudorange values are modeled as arising from the line-of-sight (LOS) distance from the satellite to the LDS receiver, plus additive terms due to additional time delays arising from propagation of the signal through the ionosphere and through the troposphere, multipath signal production and propagation, and other perturbations. These perturbations are often estimated and approximately removed by modeling the effects of such perturbations. The modeled pseudorange value for each satellite, with or without these perturbations removed, includes a square root term that models the as-yet-unknown LOS Euclidean distance. A solution for this system of pseudorange equations involves the three spatial coordinates (x,y,z) for the LDS receiver and the absolute time t (or time offset) at which the pseudorange values were measured. This solution (x,y,z,t) is conventionally estimated by iterative estimation of the system of equations or by linearized estimation of the desired solution, using a known "exact" solution (x.sub.n,y.sub.n,z.sub.n,t.sub.n) for this group of satellites that is in some sense "near" the desired solution. If this system of pseudorange equations is overdetermined, because N&gt;4 independent pseudorange values are measured, the choice of solution of this system must somehow be optimized with respect to one or more criteria related to statistical and/or geometric attributes of the pseudorange measurements.
Static error as well as drift or dynamic error in a satellite clock can be monitored and corrected for quite accurately as time changes. Static error in a receiver clock, often referred to as "clock offset," is often determined as one of the unknowns. This approach ignores the possibility that receiver error is dynamic and changes with the passage of time.
Several workers have worked with or manipulated pseudorange or a similar variable in determining the distance from a satellite, whose location as a function of time is known, to a location on or near the Earth's surface whose location coordinates are not yet known.
Counselman, in U.S. Pat. No. 4,894,662, discusses some of the problems encountered in acquiring a lock on LD signals received from GPS satellites and making accurate pseudorange measurements and discusses filtering techniques that are suitable to obtain such measurements.
U.S. Pat. No. 4,918,609, issued to Yamawaki, discloses a system that uses two geosynchronous satellites and a mobile station, referred to collectively as "stations" here, on or near the Earth's surface, each being equipped with a transmitter, receiver, antenna and clock for communication with each other. One or both satellites and the mobile station emit range-finding signals that are received by the other two stations, and each station responds by transmission of its own range-finding signal. After each station has received the response signal from the other station or stations, the receiving station determines the total time for propagation of its own transmitted signal and for propagation of the response signal from a station that received the originally transmitted signal. Time errors for the station clocks are estimated and used to synchronize the station clocks and to determine the mobile station location, if the satellite locations are known accurately. Toriyama discloses a related approach in U.S. Pat. No. 5,111,209, in which timed signals are transmitted by a fixed reference station, with known location, through two geostationary satellites to the mobile station.
A method for obtaining pseudorange measurements from encrypted P-code signals, received from GPS satellites, is disclosed by Keegan in U.S. Pat. No. 4,972,431. Use of these pseudorange measurements to obtain the location of the GPS signal receiver is not discussed in much detail.
Ames et al, in U.S. Pat. No. 5,017,926, disclose a trilateralization method for estimating the location of an LD receiver on a known surface, such as the Earth's surface, using LD signals received from two satellites with known locations and from a fictitious satellite located at the Earth's center.
In U.S. Pat. No. 5,148,179, Allison discloses use of double differences of pseudorange measurements and carrier phase measurements between first and second GPS signal receivers (one reference, one mobile) and N (.gtoreq.4) GPS satellites to determine location coordinates for a first GPS receiver. The GPS reference receiver must have known location coordinates, and this approach produces N-1 nonlinear equations that must be solved for the location coordinates and other variables.
A direction indicating system that receives and analyzes pseudorange and carrier phase signals from GPS satellites is disclosed by Durboraw in U.S. Pat. No. 5,266,958. Pseudorange signals are received at a mobile receiver and used in a conventional manner to determine receiver location. The receiver is then moved in a closed path in a selected direction, and carrier phase measurements are analyzed to provide direction parameters, such as azimuthal angle. Another direction finder, which uses a GPS omnidirectional antenna, a GPS receiver, and a directional antenna, is disclosed by Ghaem et al in U.S. Pat. No. 5,146,231.
Maki discloses use of GPS Dilution Of Precision (DOP) parameters for each visible four-satellite constellation to analyze and assign weights to the location solutions obtained for each of these constellations, in U.S. Pat. No. 5,323,163. A least squares location solution, based on the DOP-weighted four-satellite locations, is found for the GPS receiver location.
Use of a network of differential GPS reference stations to measure and construct a plurality of iso-pseudorange-correction (iso-PRC) contours associated with each visible GPS satellite is disclosed in U.S. Pat. No. 5,323,322, issued to Mueller et al. The iso-PRC contours for all visible satellites are then used to provide mathematical approximations for the differential corrections applicable to pseudorange measurements made at any location served by this network.
U.S. Pat. No. 5,359,521, issued to Kyrtsos et al, discloses analysis of pseudorange measurements at each of two or more adjacent GPS antennas, whose separation distances are precisely known, to obtain an optimized estimate of the location of one of the antennas.
Most of these approaches do not work exclusively with the pseudorange equations to determine the location coordinates of a mobile station, and some require use of geosynchronous satellites for whatever measurements are made and used. Further, these approaches do not allow straightforward location determination where the system is overdetermined (i.e., information from the satellite locations is more than is required for an exact location solution) or is under-determined, or where the receiver clock error changes substantially with time. A more useful approach would provide these advantages and would allow the user a choice of determination of the user location in which (1) information from each LD signal source is used symmetrically or (2) information from one or more LD signal sources, whose accuracy, geometric location or other attribute is enhanced relative to information from the remaining LD sources, occupies a more central position.